Three figures pray and God delights in it: Moses, David, and the Messiah. This is the claim Aggadat Bereshit makes from (Proverbs 15:8) — "the prayer of the upright is His delight." The wicked bring their sacrifices, the whole burnt offerings, the correct ritual — and it is an abomination. The righteous speak from the gut, and God leans in to hear.
Moses's prayer is called "a prayer of Moses, the man of God" (Psalm 90:1) — a title that belongs to no other figure in the Psalms. His prayer comes from a lifetime of arguing with God, pleading for a stiff-necked people, begging for entry into the land he was denied. It is the prayer of someone who has lost everything and still speaks. David's prayer comes from the other direction — a king who has everything and still needs God's vindication: "Hear, O Lord, my righteous plea; listen to my cry" (Psalm 17:1). The Messiah's prayer is different still — "a prayer of the poor man, when he is faint" (Psalm 102:1). Not a king, not a prophet. A poor man at the end of his strength.
The rabbis are building a portrait of what divine delight actually responds to. Not ritual perfection. Not high station. Not doctrinal correctness. Prayer that comes from someone who knows exactly how much they need what they're asking for — that is what moves the heavens. God hears three prayers. Each one from a different kind of righteous person. Each one a delight.